## What is Intrest

Interest, in finance and economics, is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum (that is, the amount borrowed), at a particular rate. It is distinct from a fee which the borrower may pay the lender or some third party. It is also distinct from dividend which is paid by a company to its shareholders (owners) from its profit or reserve, but not at a particular rate decided beforehand, rather on a pro rata basis as a share in the reward gained by risk taking entrepreneurs when the revenue earned exceeds the total costs.

### What is Intrest Calculator

For example, a customer would usually pay interest to borrow from a bank, so they pay the bank an amount which is more than the amount they borrowed; or a customer may earn interest on their savings, and so they may withdraw more than they originally deposited. In the case of savings, the customer is the lender, and the bank plays the role of the borrower.

Interest differs from profit, in that interest is received by a lender, whereas profit is received by the owner of an asset, investment or enterprise. (Interest may be part or the whole of the profit on an investment, but the two concepts are distinct from each other from an accounting perspective.)

The rate of interest is equal to the interest amount paid or received over a particular period divided by the principal sum borrowed or lent (usually expressed as a percentage).

Compound interest means that interest is earned on prior interest in addition to the principal. Due to compounding, the total amount of debt grows exponentially, and its mathematical study led to the discovery of the number e. In practice, interest is most often calculated on a daily, monthly, or yearly basis, and its impact is influenced greatly by its compounding rate.

## What is Interest Calculator

Our Interest Calculator can help determine the interest payments and final balances on not only fixed principal amounts, but also additional periodic contributions. There are also optional factors available for consideration such as tax on interest income and inflation. To understand and compare the different ways in which interest can be compounded, please visit our Compound Interest Calculator instead.

Interest is the compensation paid by the borrower to the lender for the use of money as a percent, or an amount. The concept of interest is the backbone behind most financial instruments in the world. While interest is earned, it is different from profit in that it is received by a lender as opposed to the owner of an asset or investment, though interest can be part of profit on an investment.

There are two distinct methods of accumulating interest, categorized into simple interest or compound interest.

### Simple Interest

The following is a basic example of how interest works. Derek would like to borrow \$100 (usually called the principal) from the bank for one year. The bank wants 10% interest on it. To calculate interest:

\$100 × 10% = \$10

This interest is added to the principal, and the sum becomes Derek's required repayment to the bank.

\$100 + \$10 = \$110

Derek owes the bank \$110 a year later, \$100 for the principal and \$10 as interest.

Let's assume that Derek wanted to borrow \$100 for two years instead of one, and the bank calculates interest annually. He would simply be charged the interest rate twice, once at the end of each year.

\$100 + \$10(year 1) + \$10(year 2) = \$120

Derek owes the bank \$120 two years later, \$100 for the principal and \$20 as interest.

The formula to calculate simple interest is:

interest = (principal) × (interest rate) × (term)

When more complicated frequencies of applying interest are involved, such as monthly or daily, use formula:

interest = (principal) × (interest rate) × (term) / (frequency)

However, simple interest is very seldom used in the real world. Even when people use the everyday word 'interest', they are usually referring to interest that compounds.

### Compound Interest

Compounding interest requires more than one period, so let's go back to the example of Derek borrowing \$100 from the bank for two years at a 10% interest rate. For the first year, we calculate interest as usual.

\$100 × 10% = \$10

This interest is added to the principal, and the sum becomes Derek's required repayment to the bank for that present time.

\$100 + \$10 = \$110

However, the year ends, and in comes another period. For compounding interest, rather than the original amount, the principal + any interest accumulated since, is used. In Derek's case:

\$110 × 10% = \$11

Derek's interest charge at the end of year 2 is \$11. This is added to what is owed after year 1:

\$110 + \$11 = \$121

When the loan ends, the bank collects \$121 from Derek instead of \$120 if it were calculated using simple interest instead. This is because interest is also earned on interest.

The more frequently interest is compounded within a time period, the higher the interest will be earned on an original principal. The following is a graph from Wikipedia showing just that, a \$1,000 investment at various compounding frequencies earning 20% interest.

There is little difference during the beginning between all frequencies, but over time they slowly start to diverge. This is the power of compound interest everyone likes to talk about, illustrated in a concise graph. Continuous compound will always have the highest return, due to its use of the mathematical limit of the frequency of compounding that can occur within a specified time period.

### The Rule of 72

Anyone who wants to estimate compound interest in their head may find the rule of 72 very useful. Not for exact calculations as given by financial calculators, but to get ideas for ballpark figures. It states that in order to find the number of years (n) required to double a certain amount of money with any interest rate, simply divide 72 by that same rate.

#### Example: How long would it take to double \$1,000 with an 8% interest rate?

n = 72/8 = 9

It will take 9 years for the \$1,000 to become \$2,000 at 8% interest. This formula works best for interest rates between 6 and 10%, but it should also work reasonably well for anything below 20%.

### Fixed vs. Floating Interest Rate

The interest rate of a loan or savings can be "fixed" or "floating". Floating rate loans or savings are normally based on some reference rate, such as the U.S. Federal Reserve (Fed) funds rate or the LIBOR (London Interbank Offered Rate). Normally, the loan rate is a little higher and the savings rate is a little lower than the reference rate. The difference goes to the profit of the bank. Both the Fed rate and LIBOR are short-term inter-bank interest rates, but the Fed rate is the main tool that the Federal Reserve uses to influence the supply of money in the U.S. economy. LIBOR is a commercial rate calculated from prevailing interest rates between highly credit-worthy institutions. Our Interest Calculator deals with fixed interest rates only.

### Contributions

An important distinction to make regarding contributions are whether they occur at the beginning or end of compounding periods. Periodic payments that occur at the end have one less interest period total per contribution.

### Tax Rate

Some forms of interest income are subject to taxes, including bonds, savings, and certificate of deposits(CDs). In the United States, corporate bonds are almost always taxed. Certain types are fully taxed while others are partially taxed; for example, while interest earned on U.S. federal treasury bonds may be taxed at the federal level, they are exempt at the state and local level. Taxes can have very big impacts on the end balance. For example, if Derek saves \$100 at 6% for 20 years, he will get:

\$100 × (1 + 6%)20 = \$320.71

This is tax-free. However, if Derek has a marginal tax rate of 25%, he will end up with \$239.78 only because the tax rate of 25% applies to each compounding period.

### Inflation Rate

Inflation is defined as an increase in the general level of prices, where a fixed amount of money will relatively afford less. The average inflation rate in the United States in the past 100 years has hovered around 3%. As a tool of comparison, the average annual return rate of the S&P 500 (Standard & Poor's) index in the United States is around 10%. Please refer to our Inflation Calculator for more detailed information about inflation.

Leave the inflation rate at 0 for quick, generalized results. But for real and accurate numbers, it is possible to input figures in order to account for inflation.

Tax and inflation combined makes it hard to grow the real value of money. For example, in the United States, the middle class has a marginal tax rate of 25% and the average inflation rate is 3%. To maintain the value of the money, a stable interest rate or investment return rate of 4% or above needs to be earned, and this is not easy to achieve.

## How to Calculate Simple Intrest

assume your deposit hundred rupees in a
bank at a rate of 10% what does this
exactly mean we know that 10% of 100 is
10 so if you deposit 100 rupees with a
bank you will get 100 10 rupees at the
end of the year but what about the
second year the third year and so on
let's make three columns the year the
interest and the total interest at the
end of the year let's also make a column
for the amount for each year so we have
four columns now and remember the amount
is the sum of the principal and the
interest the principal in this case will
be the deposit amount which is 100
rupees let's see what happens in year 1
because you get an interest of 10% from
the bank you will get 10 rupees as
interest what happens if you keep the
money with the bank for another year you
will get another 10 rupees as interest
and if you keep the hundred rupees for
one more year you again get 10 rupees as
interest that is simple interest if you
keep your money deposited with a bank
you get the same interest every year
look at it this way your principal will
remain in the bank until you withdraw it
at the end of the first year the bank
pays you an interest of 10 percent on
this 100 rupees principle that's 10
rupees these 10 rupees will accrue in
the bank until you decide to withdraw it
again at the end of the second year the
bank pays you an interest of 10 percent
on this principle 10 rupees this will
accrue until you over draw it and 10
rupees accrue again at the end of the
third year every year you get an
interest on the principal you invested
now let's look at the total interest
column if you would have taken the money
out in the first year you would have got
an interest of 10 rupees
and the amount you would have received
is hundred ten rupees
remember amount is the sum of the
principal and the interest if you would
have taken the money out in the second
year you would have got ten plus ten
which is twenty rupees an amount would
equal to hundred plus 20 which equals
one hundred twenty rupees and if you
would have taken the money out after the
third year you would have got 10 plus 10
plus 10 which is thirty rupees as
interest and an amount equal to one
hundred thirty rupees
one thing is clear the longer you keep
your money with the bank the more money
you get at the end of the period so what
are the factors that the amount is
dependent on look closely it will depend
on the principal or the initial deposit
more the money you deposit more will be
the final amount it will also depend on
the rate of interest if instead of ten
percent the bank offered you fifteen
percent the amount you receive will be
higher and of course on the number of
years you've deposited the money if any
of these factors change the amount you
would get will also change this concept
we just saw is called simple interest
the interest amount is based on the
original principal only also notice that
the total interest after the second year
is twice the interest of ten rupees and
the interest after the third year is
equal to three times the interest of ten
rupees can we deduce a formula to get
the total interest after a few years
let's consider year two we first looked
at the principal which is hundred since
the interest is 10% we multiplied it by
ten by hundred and since it is the
second young we multiplied by two this
gives us the interest in the first year
and we multiplied by two to get the
total interest after two years if you
solve this you will get a twenty and
similarly for year three the total
interest will equal
three multiplied by ten by hundred
multiplied by three this will give you
30 so based on this concept we will
solve an example in the next video
you

## How to Calculate Compound Interest?

okay so today I will introduce compound
interest with an example with the first
question over here and then you can try
question number two on your own and
after that I will explain it as well so
here is the compound interest formula
and it will clarify each element that we
have here the B will be the initial
amount invested a will be the final
amount so so far so good right R will be
the interest rate n will be the amount
of times that the investment is
compounded per year so that's a pretty
important value we have two of them in
the formula for example if in the in the
first example here we have annual
compounding right which means that n
would be one because it's compounded
only once a year
and finally the T of course is time you
should be writing this now maybe you
already are so here's the interest rate
interest rate time n is the number of
times the compounds per year
well my handwriting is horrible today
and P is the initial amount of money a
is the final amount of money so for
question number one here I have a
thousand dollars invested at five
percent compounded annually so a is what
we want to find out P is a thousand then
I have one plus R which is five percent
and since we have five percent I'll need
to rewrite this as 0.05 okay all I need
to do is just divide the 5 by 100 so we
have point zero five divided by one
that's because it's annual compounding
for the next one already give you a hint
for monthly compounding n is going to be
twelve because then the investment is
compounded twelve times a year so then
in this case we have this ^ time in this
case times seven seven years and time is
going to multiply the N and n is one
just like it was one over here so let me
just make this look a little bit better
point zero five little bit divided by 1
is just 0.2 0 5 plus 1 is one point zero
5 ^ 7 because 7 times 1 is just 7 great
now what do we do one very common
mistake is for people to multiply the
1000 by the 1.05 we can't do that
because of PEMDAS right we have to do
exponents before multiplication so we're
going to do one point zero 5 ^ 7 first
and let me use my calculator to figure
that out so we get one point four zero
seven then we can multiply that by a
thousand and we get the final amount of
one thousand four hundred and seven
dollars and ten cents okay so after
seven years investing at five percent
compounded annually a thousand dollars
becomes a thousand or one hundred and
seven dollars and ten cents great now I
will suggest that you try question
number two on your own if you want you
can pause the video

you
and now it will explain it so I'm pretty
cleared up all the elements that we have
here a little different letters and so
in this case we have a is equal to B the
initial amount is two thousand dollars
invested at 12% compounded monthly so to
12 percent we're going to plug it in
here for our but we're going to write it
as 0.12
because it's a percentage right so 12
divided by 100 is 0.12 now divided by N
and is 12 because it's monthly
compounding so it compounds 12 times a
year to the power of T is 5 because
we're investing this for 5 years and
we're multiplying the 5 by 12 because
that's n again so we have a equals 2000
times now point 12 divided by 12 is 0.01
plus 1 is one point zero 1 to the power
of 60 again very popular mistake please
avoid it be to multiply the two thousand
by the 1.01 right away we can't do that
because we need to do this first we need
to go one point zero one to the power of
60 and on we get one point eight one six
seven for that so we do this first and
then we multiply that value by two
thousand two obtain three thousand six
hundred and thirty three dollars and
thirty nine cents so that's it so
investing two thousand dollars at 12%
compounded monthly for five years this
is what we get so hopefully that make
great sense to you and check up some
more videos right here good luck

## How Bank Calculate Intrest

Last week we talked about NUT.
and i was assuming that everybody knows how to calculate compound interest.
70% don't know how to calculate compound interest.
I guess we learned compound intererst from 7-8th class.
It's very basic
If you deposit money in bank account so the interest you get is compound interest.
SO if you don't know how to calculate this.
This is wrong. You should know.
Where you are investing , you are supposed to aware how much interest you'll get.
Let's understand this on white board
How to calculate compound interest.
Let's say i gave 1000 to someone , so what will be the value after 1 year.
at a interest of 10%
100 rs will be simple interest.
So i got 1100rs after 1 year with interest.
Next year again i'll get 100rs interest.
But logically
Next year i gave them 1100rs right?
So 100 won't be the interest according to 1100rs.
1000 + 100 = 1100rs
So in second year i should get interest at 1100rs not 1000rs.
But the bank gave 100rs interest.
Logically they should've given 110rs.
But Bank gave 100rs.
That's why simple interest formula didn't work after 1 year.
Now advanced thing i.e Compound interest.
In Compound interest you're getting 110rs in second year.
So in 1 st year you get 100rs
Next year you get 110rs.
100 + 10% of 100 = 110.
Means overall you get 110rs.
In third year , you get 100 + 10% of 110rs = calculate ;p
So if you want to calculate for 10 year then?
THis is the formula for compound interest.
P = principal amount
Like here P=1000
R is rate of interest
Rate = 10%
N = No. of year
Now what we calculated here.
Here we took the value of n = 1,2,3......
It means we are calculating compound interest manually.
You'll see somewhere that 10% compounded annually.
means 1,2,3.......
If it's compounded monthly
Then you need to calculate in terms of months.
Like you are investing somewhere for 5 years
So there are 12 months in 1 year
12*5 = 60 months
Calculate the compound interest monthly.
Your value n is 60 here.
and rate is annual rate
Let's say 12%
What we will do rate-12/12(months)
So logically rate of interest is 1% monthly.
12/12
That is 1 % of rate of interest.
Same formula of compound interest.
and then after dividing the denominator with numerator ,
and then we'll multiply that with n
That's it.
If you still didn't understand it, tell me in the comments below.
i may make an another video
I will upload a video today in the evening .It might be controversial.
I hope you'll support me.
Okat friends(dosto) , with this, video ends. I hope you liked it.
Like share and do tell me in the comments.
Did you know how to calculate compound interest?
do tell me
If you haven't seen that NUT video.
You can check how do we calculate interest.
Here we talked about compound interest.
That we invested 1000rs in 1 year.
How much will i get after 10 years.
But if we are investing 1000 rs every year
Interest will keep on increasing.
How do we calculate that
Whether it's profitable for you or not?